Question

1. paul paints houses. he charges his customers a fixed amount to cover the expenses of using a paint sprayer and buying brushes. he also charges an amount based on the number of gallons of paint (x) he will need. the equation shown below represents the total amount (y), in dollars, paul charges his customers for the materials he will need for a job. y = 14.5x + 80. what is represented by the number 14.5 in pauls equation? a. the number of gallons of paint paul will need b. the charge for each gallon of paint paul will need c. the number of hours it will take to complete the paint job d. the fixed amount charged for using a paint sprayer and buying brushes. 14) pia makes bouquets so there is a proportional relationship between the number of roses and the number of carnations in the bouquet. her first bouquet has 9 roses and 15 carnations. which of the following does not have the same proportional relationship between the number of roses and carnations? a) 12 roses and 20 carnations b) 21 roses and 30 carnations c) 15 roses and 25 carnations d) 24 roses and 40 carnations. 15) what is the x and y - intercepts for 2x - 4y = 20? list answers as ordered pairs. 16) explain why the slope of the line that passes through the points (-6, 5) and (9, 5) is 0. 17) a local restaurant offers a \build your own salad\ where you pay a fixed price for the base (mixed greens) and an additional fee for each topping added to the salad. tanesha orders a medium salad with cucumbers, tomatoes, onions and cheese and pays $12.25. dylan orders a medium salad with cucumbers and tomatoes and pays $9.25. a. how much is each additional topping?

Explanation:

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Step1: Analyze the linear - equation form

The equation is in the form $y = mx + b$, where $y$ is the total amount, $x$ is the number of gallons of paint, $m$ is the slope, and $b$ is the y - intercept.

Step2: Identify the meaning of 14.5

In the equation $y = 14.5x+80$, 14.5 is the coefficient of $x$ (the number of gallons of paint). It represents the change in $y$ (total cost) for each unit change in $x$ (one - gallon increase in paint). So, it is the charge for each gallon of paint.

Step1: Find the ratio in the first bouquet

The ratio of roses to carnations in the first bouquet is $\frac{9}{15}=\frac{3}{5}$.

Step2: Check each option

• Option A: $\frac{12}{20}=\frac{3}{5}$
• Option B: $\frac{21}{30}=\frac{7}{10}

eq\frac{3}{5}$

• Option C: $\frac{15}{25}=\frac{3}{5}$
• Option D: $\frac{24}{40}=\frac{3}{5}$

Step1: Find the x - intercept

Set $y = 0$ in the equation $2x-4y = 20$. Then $2x-4(0)=20$, which simplifies to $2x=20$ and $x = 10$. So the x - intercept is the ordered pair $(10,0)$.

Step2: Find the y - intercept

Set $x = 0$ in the equation $2x - 4y=20$. Then $2(0)-4y=20$, which simplifies to $-4y=20$ and $y=-5$. So the y - intercept is the ordered pair $(0, - 5)$.

Answer:

B. the charge for each gallon of paint Paul will need

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